A finite element method for magma-rock interaction dynamics in volcanic environment

Underground magmatic processes and their effects on the Earth’s surface are an issue that requires advanced models to be unrevealed. The comprehension of the mutual link between magma and rock is crucial for the advancement in understanding of the physics of volcanoes and the associated hazard. In this thesis, a numerical method for magma-rock interaction (Fluid Structure Inter-action, FSI) problem has been developed in order to understand the processes of magma dynamics in magma chambers. A segregated algorithm by means of finite elements method (FEM) is used to solve the FSI problem, where the fluid and structure domains are interconnected by a standard sequence of transfer of boundary conditions. After validation, the numerical algorithm is applied to model the magma flow in chambers. Magma is assumed to have a compressible/incompressible multicomponent single-phase flow. Magma properties are computed as a function of the local P-T-X conditions with the proper constitutive equations. Three simulation cases of natural convection and magma mixing occurring inside magma chambers are presented. The first case studies the Rayleigh-Taylor instability arose between two stratified layers (hot and cold) of a magma in an elliptical chamber. The second case examines the mixing between two heterogeneous magmas placed in the shallower and deeper reservoirs, connected through a vertical dike. The last case analyses the magma mixing in the presence of a seismic excitation. All simulations include the convection driven by buoyancy forces solely. The numerical results reveal that the viscosity of magma plays a crucial role in magma mixing. Depending on the magma viscosity, the time-scale of convection and mixing can vary from a few hours to tens of hours. The simulation results show that the magma mixing caused by the pure buoyant forces causes a decompression in the shallower chamber. The results also illustrate that the impinge of a seismic wave has no influence on the magma mixing, but, it is able to increase the overpressure in the magmatic system.